Field
Embodiments described herein relate generally to a method of reconstructing computed tomography (CT) images by averaging nearest-neighbor CT images, and more specifically to averaging nearest-neighbor tilted CT images in order to reconstruct tilted CT images having a thickness greater than the slice thickness corresponding to the projection data.
Description of the Related Art
Computed tomography (CT) systems and methods are widely used, particularly for medical imaging and diagnosis. CT systems generally create images of one or more sectional slices through a subject's body. A radiation source, such as an X-ray source, irradiates the body from one side. A collimator, generally adjacent to the X-ray source, limits the angular extent of the X-ray beam, so that radiation impinging on the body is substantially confined to a planar region defining a cross-sectional slice of the body. At least one detector (and generally many more than one detector) on the opposite side of the body receives radiation transmitted through the body substantially in the plane of the slice. The attenuation of the radiation that has passed through the body is measured by processing electrical signals received from the detector.
FIG. 1A shows a CT sinogram, which is a plot of attenuation through the body as a function of “space” along a detector array (horizontal) and “time/angle” of a scan of measurements performed at a series of projection angles (vertical). The space dimension refers to the position along a one-dimensional array of X-ray detectors. The time/angle dimension refers to the projection angle of X-rays changing as a function of time, such that as time progresses the projection angle increments and projection measurements are performed at a linear succession of projection angles. The attenuation resulting from a particular volume will trace out a sine wave around the vertical axis—volumes farther from the axis of rotation having sine waves with larger amplitudes, the phase of a sine wave determining the volume's angular position around the rotation axis. Performing an inverse Radon transform or equivalent image reconstruction method reconstructs an image from the projection data in the sinogram—the reconstructed image corresponding to a cross-sectional slice of the body, as shown in FIG. 1A.
The process of X-ray projection measurements of two-dimensional slices through an object onto a one-dimensional measurement plane can be represented mathematically as a Radon transformationg(X,z)=R[f(x,y,z)],where g(X,z) is the projection data as a function of position X along a detector array for a slice of thickness dz normal to the z-direction, f(x,y,z) is the attenuation of the object as a function of position, and R[·] is the Radon transform in the x-y plane. Having measured projection data at multiple angles, the image reconstruction problem can be expressed by calculating the inverse Radon transformation of the projection dataf(x,y,z)=R−1[g(X,z,θ)],where R−1 [·] is the inverse Radon transform and θ is the projection angle at which the projection data was acquired. In practice, there are many methods for reconstructing an image f(x,y,z) from the projection data g(X,z,θ).
Often the image reconstruction problem will be formulated as a matrix equationAf=g,where g represents the projection measurements of the X-rays transmitted through an object space including the object OBJ, A is the system matrix describing the discretized line integrals (i.e., the Radon transforms) of the X-rays through the object space, and f is the image of object OBJ (i.e., the quantity to be solved for by solving the system matrix equation). Image reconstruction can be performed by taking the matrix inverse or pseudo-inverse of the matrix A. However, this rarely is the most efficient method for reconstructing an image. The more conventional approach is called filtered back projection (FBP), which consistent with the name, entails filtering the projection data and then back projecting the filtered projection data onto the image space, as expressed byf(x,y,z)=BP[g(X,z,θ)*FRamp(X)].where FRamp(X) is a ramp filter (the name “ramp filter” arises from its shape in the spatial-frequency domain), the symbol * denotes convolution, and BP[·] is the back projection function.
Other methods of image reconstruction include: iterative reconstruction methods (e.g., the algebraic reconstruction technique (ART) method and the total variation minimization regularization methods), Fourier-transform-based methods (e.g., direct Fourier method), and statistical methods (e.g., maximum-likelihood expectation-maximization algorithm based methods).
While it is known how to reconstruct CT images from projection data corresponding to a given projection plane using, e.g., the iterative or filtered-back-projection methods discussed above, in some applications it is desirable to combine projection data from several adjacent thin-slice CT scans to generate a single thick-slice CT image. When the translation direction between CT scans is orthogonal to the projection planes, reconstructing a thick-slice image from thin-slice projection data can be realized by the straightforward process of averaging the projection data into thick slices and then reconstructing an image from the resulting thick-slice projection data. However, when the projection planes of the CT scans are tilted with respect to the translation direction, an offset due to the tilt can create complications in reconstructing a thick-slice image from the tilted thin-slice projection data.